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\begin{document}

\title{Correcting Physics-Based Global Tide and Storm Water Level Forecasts
with the Temporal Fusion Transformer}



\author[1]{Albert R Cerrone}%
\author[1]{Leendert G Westerink}%
\author[2]{Guoming Ling}%
\author[1]{Coleman Peter Blakely}%
\author[1]{Damrongsak Wirasaet}%
\author[3]{Clint Dawson}%
\author[1]{Joannes Westerink}%
\affil[1]{University of Notre Dame}%
\affil[2]{Tohoku University}%
\affil[3]{University of Texas at Austin}%


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  \date{May 16, 2024}


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\begin{abstract}
Global and coastal ocean surface water elevation prediction skill has
advanced considerably with improved algorithms, more refined
discretizations and high-performance parallel computing. Model skill is
tied to mesh resolution, the accuracy of specified
bathymetry/topography, dissipation parameterizations, air-sea drag
formulations, and the fidelity of forcing functions. Wind forcing skill
can be particularly prone to errors, especially at the land-ocean
interface. The resulting biases and errors can be addressed holistically
with a machine-learning (ML) approach. Herein, we weakly couple the
Temporal Fusion Transformer to the National Oceanic and Atmospheric
Administration's (NOAA) Storm and Tide Operational Forecast System
(STOFS 2D Global) to improve its forecasting skill throughout a 7-day
horizon. We demonstrate the transformer's ability to enrich the
hydrodynamic model's output at 228 observed water level stations
operated by NOAA's National Ocean Service. We conclude that the
transformer is a rapid way to correct STOFS 2D Global forecasted water
levels provided that sufficient covariates are supplied. For stations in
wind-dominant areas, we demonstrate that including past and future
wind-speed covariates make for a more skillful forecast. In general,
while the transformer renders consistent corrections at both tidally and
wind-dominant stations, it does so most aggressively at tidally-dominant
stations. We show notable improvements in Alaska and the Atlantic and
Pacific seaboards of the United States. We evaluate several transformers
instantiated with different hyperparameters, covariates, and training
data to provide guidance on how to enhance performance.%
\end{abstract}%



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